<script type="text/javascript"
     src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
</script>

<font size="6" color="Magenta">Steady-State Tip Clearance Library Block</font>
<br>
<p>This block produces the steady-state tip clearance inside turobmachinery for a given 
operating condition. That is to say that it provides the tip clearance and relavant 
temperatures and lengths of components once all dynamics have resided. This block is useful 
for initializing the 
<a href="DynTipClearance.html">Dynamic Tip Clearance</a> 
block. It is also useful for evaluating steady-state tip clearance and engine performance 
impact on-the-fly. When evaluating performance impact using the 
<a href="TipClearEffPerf.html">Tip Clearance Effect on Performance</a> 
block for an "off-nominal" turbine conguration (configuration refers to the combination of
dimensions, materials, etc. that define the turbine), this block should be used to define the 
nominal tip clearance that is fed into the 
<a href="TipClearEffPerf.html">Tip Clearance Effect on Performance</a> 
block. In this case, the inputs of the Steady-State Tip Clearance block should be the 
same as the 
<a href="DynTipClearance.html">Dynamic Tip Clearance</a> 
block, but the block parameters should reflect the nominal turbine design.

<p>This function approximates axisymmetric tip clearance variation inside turbomachinery 
(i.e. compressors and turbines). It models the deformation of the rotor disc, blade, and engine casing/shroud 
(containment structure) due to elastic thermal and centrifugal deformation. The blade is 
modeled as a lumped mass and the rotor disc and engine casing use a 1-D finite difference approach for 
temperature determination. The shroud is assumed to be offset from the engine casing by a fixed
distance. Since the engine casing provides the structural support for the shroud, the shroud 
displacement is based on the engine casing deformation. The thermal deformation models use the 
average component temperature. 
This function has numerous options for modeling convective heat transfer coefficients and 
temperature dependence of various parameters including thermal conductivity, heat capacity, 
thermal expansion coefficient, Young's Modulus, and Poisson's ratio. If temperature dependent 
thermal properties are specified then the average temperature of the component is calculated, 
the thermal property is chosen based on the average temperature, the steady-state solution is 
evaluated with this constant thermal property value, and the solution is iterated on until it 
converges.<p>

<p>Centrifugual deformations are based on static equations which require no additional consideration 
to get a steady-state solution. However, the thermal deformation is dependent on temperature which 
is governed by differential equations. The theoretical steady-state solution is evaluated for each 
of the components. In the case of the blade the steady-state blade temperature is equal to the 
reference temperature which is between the core flow temperature and temperature of the blades cooling 
flow. The value of the reference temperature is dependent on the film cooling coefficient. An expression 
for the reference temperature is given in 
<a href="DynTipClearance.html">Dynamic Tip Clearance</a>.
The rotor is modeled as a 1-D planar slab and the engine casing is modeled as an infinite cylindrical shell. 
Theoretical solutions based on a lumped thermal resistance model can be found in text books and other 
resources. <p>

<p>All inputs and parameters (masked variables) are in standard English units. The units are indicated 
in the tables below as well as the block cover and dialog box. Outputs are in standard English units 
with the exception of the tip clearance which is in mils (1mil = 0.001in).<p>
    
<p>Given this block is a steady-state version of the
<a href="DynTipClearance.html">Dynamic Tip Clearance</a> 
block, it's help menu can be referred to for various details.<p>

<br>
<font size="5" color="Blue">Dynamic Tip Clearance Inputs:</font>
<table border="1"> <tr><td>Tip Clearance Input</td><td>Description</td></tr>
    <tr><td>Nmech</td><td>shaft speed [rpm]</td></tr>
	<tr><td>Tcore - Blade</td><td>temperature of the flow inside the core that is exposed to the blade (neglecting film cooling) [degR]</td></tr>
	<tr><td>Tcool - Blade</td><td>temperature of the flow used for film cooling [degR]</td></tr>
	<tr><td>Tcool - Rotor Front</td><td>temperature of the flow used to cool the front of the rotor disc [degR]</td></tr>
	<tr><td>Wcool - Rotor Front</td><td>mass flow rate of the flow used to cool the front of the rotor disc [slug/sec]</td></tr>
	<tr><td>Tcool - Rotor Back</td><td>temperature of the flow used to cool the back of the rotor disc [degR]</td></tr>
	<tr><td>Wcool - Rotor Back</td><td>mass flow rate of the flow used to cool the back of the rotor disc [slug/sec]</td></tr>
	<tr><td>Tin - Case</td><td>temperature of the flow on the inner surface of the engine case [degR]</td></tr>
    <tr><td>Win - Case</td><td>mass flow rate of the flow used to cool the inner surface of the engine case [slug/sec]</td></tr>
    <tr><td>Tout - Case</td><td>temperature of the flow on the outer surface of the engine case [degR]</td></tr>
    <tr><td>Wout - Case</td><td>mass flow rate of the flow used to cool the outer surface of the engine case [slug/sec]</td></tr>
	<tr><td>Wout Nom - Case</td><td>nominal mass flow rate of the flow used to cool the outer surface of the engine case (defined by the nominal cooling schedule) [slug/sec]</td></tr>
</table>
<br>
<font size="5" color="Blue">Dynamic Tip Clearance Outputs:</font>
<table border="1"> <tr><td>Tip Clearance Output</td><td>Description</td></tr>
    <tr><td>Out</td><td>Tip Clearance Output, structure consisting of 1 variable and 3 substructions:
            <br>- TC - tip clearance [mils]
            <br>- TCnom - nominal tip clearance (considering nominal cooling) [mils]
            <br>- Case
			<br>---- T - array containing the temperature solution for the engine case [degR]
			<br>---- Tavg - average temperature of the engine case [degR]
			<br>---- L - inner radius of the case [ft]
            <br>---- Lnom - nominal inner radius of the case (considering nominal cooling) [ft]
			<br>- Blade
			<br>---- T - temperature of the blade [degR]
			<br>---- L - length of the blade [ft]
            <br>---- Lu - unstrained length of the blade (without considering centrifugal expansion) [ft]
			<br>- Rotor
			<br>---- T - array containing the temperature solution for the rotor disc [degR]
			<br>---- Tavg - average temperature of the rotor disc [degR]
			<br>---- L - outer radius of the rotor disc [ft] 
            <br>---- Lu - unstrained outer radius of the rotor disc (without considering centrifugal expansion) [ft]
</table>
<br>
<font size="5" color="Blue">Dynamic Tip Clearance Mask Variables: </font>
<table border="1"> <tr><td>Turbine Mask Variable</td><td>Description</td></tr>
	<tr><td>eta_Blade_M</td><td>film cooling coefficient for cooling of the blade [frac]</td></tr>
	<tr><td>T0_Blade_M</td><td>initial temperature of the blade [degR]</td></tr>
	<tr><td>dt_Blade_M</td><td>time-step for solving for the blade temperature state and sampling time of the blocks involved with this calculation [sec]</td></tr>
	<tr><td>h_Const_Blade_M</td><td>check to use the constant h_Blade_M as the convective heat transfer coefficient for the blade</td></tr>
	<tr><td>h_Eqn_Blade_M</td><td>check to use the equation h = hcoeff*(T/Tdes)^0.23*(W/Wdes)^0.8 to determine the convective heat transfer coefficient for the blade</td></tr>
	<tr><td>h_Data_Blade_M</td><td>check to use the data arrays Wc_Blade_Data_M, Tc_Blade_Data_M, and h_Blade_Data_M to interpolate the convective heat transfer coefficient for the blade</td></tr>
	<tr><td>h_Blade_M</td><td> constant convective heat transfer coefficient for the blade [Btu/(sec-ft^2-degR)]</td></tr>
	<tr><td>hcoeff_Blade_M</td><td> coefficient in the equation h = hcoeff*(T/Tdes)^0.23*(W/Wdes)^0.8 used to evaluate the convective heat transfer coefficient for the blade [Btu/(sec-ft^2-degR)]</td></tr>
	<tr><td>Wdes_Blade_M</td><td> mass flow rate at a design point (known point) used to normalize the mass flow rate in the convective heat transfer coefficient model for the blade [slug/sec]</td></tr>
	<tr><td>Tdes_Blade_M</td><td> temperature at a design point (known point) used to normalize the temperature in the convective heat transfer coefficient model for the blade [degR]</td></tr>
	<tr><td>Wc_Blade_Data_M</td><td> Non-dimensional mass flow rate (W/Wdes) array used in interpolating the convective heat transfer coefficient for the blade [-] (bx1)</td></tr>
	<tr><td>Tc_Blade_Data_M</td><td> Non-dimensional temperature (T/Tdes) array used in interpolating the convective heat transfer coefficient for the blade [-] (cx1) </td></tr>
	<tr><td>h_Blade_Data_M</td><td> Matrix of convective heat transfer coefficients for the blade  rows corresponding to Wc_Blade_Data_M and columns corresponding to Tc_Blade_Data_M [Btu/(sec-ft^2-degR)] (bxc)</td></tr>
	<tr><td>L_Blade_M</td><td>length of the blade [ft]</td></tr>
	<tr><td>rho_Blade_M</td><td>density of the blade [slug/ft^3]</td></tr>
	<tr><td>alpha_TempDependence_Blade_M</td><td>temperature dependence of the thermal expansion coefficient of the blade. When unchecked the constant thermal expansion coefficient alpha_Blade_M is used and when checked the thermal expansion coefficient is interpolated each time-step based on temperature and thermal expansion coefficient data given by Talpha_Blade_Data_M and alpha_Blade_Data_M</td></tr>
	<tr><td>alpha_Blade_M</td><td>constant thermal expansion coefficient for the blade [1/degR)]</td></tr>
	<tr><td>Talpha_Blade_Data_M</td><td>temperature array for interpolating the thermal expansion coefficient of the blade [degR] (dx1)</td></tr>
	<tr><td>alpha_Blade_Data_M</td><td>thermal expansion coefficient array correspondeing to Talpha_Blade_Data_M for interpolating the thermal expansion coefficient of the blade [1/degR] (dx1)</td></tr>
	<tr><td>E_TempDependence_Blade_M</td><td>temperature dependence of Young's Modulus of the blade. When unchecked the constant Young's Modulus E_Blade_M is used and when checked Young's Modulus is interpolated each time-step based on temperature and Young's Modulus data given by TE_Blade_Data_M and E_Blade_Data_M</td></tr>
	<tr><td>E_Blade_M</td><td>constant Young's Modulus for the blade [lbf/ft^2]</td></tr>
	<tr><td>TE_Blade_Data_M</td><td>temperature array for interpolating Young's Modulus of the blade [degR] (ex1)</td></tr>
	<tr><td>E_Blade_Data_M</td><td>Young's Modulus array correspondeing to TE_Blade_Data_M for interpolating Young's Modulus of the blade [lbf/ft^2] (ex1)</td></tr>
	<tr><td>W_Rotor_M</td><td>width of the rotor from front to back [ft]</td></tr>
	<tr><td>n_Rotor_M</td><td>number of nodes in the spatial discretization of the rotor</td></tr>
	<tr><td>T0_Rotor_M</td><td>initial temperatures array for the rotor [degR] (n_Rotor_Mx1)</td></tr>
	<tr><td>rho_Rotor_M</td><td>density of the rotor [slug/ft^3]</td></tr>
	<tr><td>k_TempDependence_Rotor_M</td><td>temperature dependence of the thermal conductivity of the rotor. When unchecked the constant thermal conductivity k_Rotor_M is used and when checked the thermal conductivity is interpolated each time-step based on temperature and thermal conductivity data given by Tk_Rotor_Data_M and k_Rotor_Data_M</td></tr>
	<tr><td>k_Rotor_M</td><td>constant thermal conductivity for the rotor [Btu/(sec-ft-degR)]</td></tr>
	<tr><td>Tk_Rotor_Data_M</td><td>temperature array for interpolating the thermal conductivity of the rotor [degR] (fx1)</td></tr>
	<tr><td>k_Rotor_Data_M</td><td>thermal conductivity array correspondeing to Tk_Rotor_Data_M for interpolating the thermal conductivity of the rotor [Btu/(sec-ft-degR)] (fx1)</td></tr>
	<tr><td>h_Const_Rotor_Front_M</td><td>check to use the constant h_Rotor_Front_M as the convective heat transfer coefficient for the front surface of the rotor</td></tr>
	<tr><td>h_Eqn_Rotor_Front_M</td><td>check to use the equation h = hcoeff*(T/Tdes)^0.23*(W/Wdes)^0.8 to determine the convective heat transfer coefficient for the front surface of the rotor</td></tr>
	<tr><td>h_Data_Rotor_Front_M</td><td>check to use the data arrays Wc_Rotor_Front_Data_M, Tc_Rotor_Front_Data_M, and h_Rotor_Front_Data_M to interpolate the convective heat transfer coefficient for the front surface of the rotor</td></tr>
	<tr><td>h_Rotor_Front_M</td><td> constant convective heat transfer coefficient for the front surface of the rotor [Btu/(sec-ft^2-degR)]</td></tr>
	<tr><td>hcoeff_Rotor_Front_M</td><td> coefficient in the equation h = hcoeff*(T/Tdes)^0.23*(W/Wdes)^0.8 used to evaluate the convective heat transfer coefficient for the front surface of the rotor [Btu/(sec-ft^2-degR)]</td></tr>
	<tr><td>Wdes_Rotor_Front_M</td><td> mass flow rate at a design point (known point) used to normalize the mass flow rate in the convective heat transfer coefficient model for the front surface of the rotor [slug/sec]</td></tr>
	<tr><td>Tdes_Rotor_Front_M</td><td> temperature at a design point (known point) used to normalize the temperature in the convective heat transfer coefficient model for the front surface of the rotor [degR]</td></tr>
	<tr><td>Wc_Rotor_Front_Data_M</td><td> Non-dimensional mass flow rate (W/Wdes) array used in interpolating the convective heat transfer coefficient for the front surface of the rotor [-] (hx1)</td></tr>
	<tr><td>Tc_Rotor_Front_Data_M</td><td> Non-dimensional temperature (T/Tdes) array used in interpolating the convective heat transfer coefficient for the front surface of the rotor [-] (ix1) </td></tr>
	<tr><td>h_Rotor_Front_Data_M</td><td> Matrix of convective heat transfer coefficients for the front surface of the rotor with rows corresponding to Wc_Rotor_Front_Data_M and columns corresponding to Tc_Rotor_Front_Data_M [Btu/(sec-ft^2-degR)] (hxi)</td></tr>
	<tr><td>h_Const_Rotor_Back_M</td><td>check to use the constant h_Rotor_Front_M as the convective heat transfer coefficient for the back surface of the rotor</td></tr>
	<tr><td>h_Eqn_Rotor_Back_M</td><td>check to use the equation h = hcoeff*(T/Tdes)^0.23*(W/Wdes)^0.8 to determine the convective heat transfer coefficient for the back surface of the rotor</td></tr>
	<tr><td>h_Data_Rotor_Back_M</td><td>check to use the data arrays Wc_Rotor_Front_Data_M, Tc_Rotor_Front_Data_M, and h_Rotor_Front_Data_M to interpolate the convective heat transfer coefficient for the back surface of the rotor</td></tr>
	<tr><td>h_Rotor_Back_M</td><td> constant convective heat transfer coefficient for the back surface of the rotor [Btu/(sec-ft^2-degR)]</td></tr>
	<tr><td>hcoeff_Rotor_Back_M</td><td> coefficient in the equation h = hcoeff*(T/Tdes)^0.23*(W/Wdes)^0.8 used to evaluate the convective heat transfer coefficient for the back surface of the rotor [Btu/(sec-ft^2-degR)]</td></tr>
	<tr><td>Wdes_Rotor_Back_M</td><td> mass flow rate at a design point (known point) used to normalize the mass flow rate in the convective heat transfer coefficient model for the back surface of the rotor [slug/sec]</td></tr>
	<tr><td>Tdes_Rotor_Back_M</td><td> temperature at a design point (known point) used to normalize the temperature in the convective heat transfer coefficient model for the back surface of the rotor [degR]</td></tr>
	<tr><td>Wc_Rotor_Back_Data_M</td><td> Non-dimensional mass flow rate (W/Wdes) array used in interpolating the convective heat transfer coefficient for the back surface of the rotor [-] (jx1)</td></tr>
	<tr><td>Tc_Rotor_Back_Data_M</td><td> Non-dimensional temperature (T/Tdes) array used in interpolating the convective heat transfer coefficient for the back surface of the rotor [-] (kx1) </td></tr>
	<tr><td>h_Rotor_Back_Data_M</td><td> Matrix of convective heat transfer coefficients for the back surface of the rotor with rows corresponding to Wc_Rotor_Front_Data_M and columns corresponding to Tc_Rotor_Front_Data_M [Btu/(sec-ft^2-degR)] (jxk)</td></tr>
	<tr><td>Ro_Rotor_M</td><td>outer radius of the rotor [ft]</td></tr>
	<tr><td>alpha_TempDependence_Rotor_M</td><td>temperature dependence of the thermal expansion coefficient of the rotor. When unchecked the constant thermal expansion coefficient alpha_Rotor_M is used and when checked the thermal expansion coefficient is interpolated each time-step based on temperature and thermal expansion coefficient data given by Talpha_Rotor_Data_M and alpha_Rotor_Data_M</td></tr>
	<tr><td>alpha_Rotor_M</td><td>constant thermal expansion coefficient for the rotor [1/degR)]</td></tr>
	<tr><td>Talpha_Rotor_Data_M</td><td>temperature array for interpolating the thermal expansion coefficient of the rotor [degR] (lx1)</td></tr>
	<tr><td>alpha_Rotor_Data_M</td><td>thermal expansion coefficient array correspondeing to Talpha_Rotor_Data_M for interpolating the thermal expansion coefficient of the rotor [1/degR] (lx1)</td></tr>
	<tr><td>E_TempDependence_Rotor_M</td><td>temperature dependence of Young's Modulus of the rotor. When unchecked the constant Young's Modulus E_Rotor_M is used and when checked Young's Modulus is interpolated each time-step based on temperature and Young's Modulus data given by TE_Rotor_Data_M and E_Rotor_Data_M</td></tr>
	<tr><td>E_Rotor_M</td><td>constant Young's Modulus for the rotor [lbf/ft^2]</td></tr>
	<tr><td>TE_Rotor_Data_M</td><td>temperature array for interpolating Young's Modulus of the rotor [degR] (mx1)</td></tr>
	<tr><td>E_Rotor_Data_M</td><td>Young's Modulus array correspondeing to TE_Rotor_Data_M for interpolating Young's Modulus of the rotor [lbf/ft^2] (mx1)</td></tr>
	<tr><td>v_TempDependence_Rotor_M</td><td>temperature dependence of Poisson's ratio of the rotor. When unchecked the constant Poisson's ratio v_Rotor_M is used and when checked Poisson's ratio is interpolated each time-step based on temperature and Poisson's ratio data given by Tv_Rotor_Data_M and v_Rotor_Data_M</td></tr>
	<tr><td>v_Rotor_M</td><td>constant Young's Modulus for the rotor [-]</td></tr>
	<tr><td>Tv_Rotor_Data_M</td><td>temperature array for interpolating Poisson's ratio of the rotor [degR] (nx1)</td></tr>
	<tr><td>v_Rotor_Data_M</td><td>Poisson's ratio array correspondeing to Tv_Rotor_Data_M for interpolating Poisson's ratio of the rotor [-] (nx1)</td></tr>'
	<tr><td>W_Case_M</td><td>width of the engine case [ft]</td></tr>
	<tr><td>n_Case_M</td><td>number of nodes in the spatial discretization of the engine case</td></tr>
	<tr><td>T0_Case_M</td><td>initial temperatures array for the engine case [degR] (n_Case_Mx1)</td></tr>
    <tr><td>rho_Case_M</td><td>density of the engine case [slug/ft^3]</td></tr>
	<tr><td>k_TempDependence_Case_M</td><td>temperature dependence of the thermal conductivity of the engine case. When unchecked the constant thermal conductivity k_Case_M is used and when checked the thermal conductivity is interpolated each time-step based on temperature and thermal conductivity data given by Tk_Case_Data_M and k_Case_Data_M</td></tr>
	<tr><td>k_Case_M</td><td>constant thermal conductivity for the engine case [Btu/(sec-ft-degR)]</td></tr>
	<tr><td>Tk_Case_Data_M</td><td>temperature array for interpolating the thermal conductivity of the enigne case [degR] (ox1)</td></tr>
	<tr><td>k_Case_Data_M</td><td>thermal conductivity array correspondeing to Tk_Case_Data_M for interpolating the thermal conductivity of the engine case [Btu/(sec-ft-degR)] (ox1)</td></tr>
	<tr><td>h_Const_Case_In_M</td><td>check to use the constant h_Case_In_M as the convective heat transfer coefficient for the inner surface of the engine case</td></tr>
	<tr><td>h_Eqn_Case_In_M</td><td>check to use the equation h = hcoeff*(T/Tdes)^0.23*(W/Wdes)^0.8 to determine the convective heat transfer coefficient for the inner surface of the engine case</td></tr>
	<tr><td>h_Data_Case_In_M</td><td>check to use the data arrays Wc_Case_In_Data_M, Tc_Case_In_Data_M, and h_Case_In_Data_M to interpolate the convective heat transfer coefficient for the inner surface of the engine case</td></tr>
	<tr><td>h_Case_In_M</td><td> constant convective heat transfer coefficient for the inner surface of the engine case [Btu/(sec-ft^2-degR)]</td></tr>
	<tr><td>hcoeff_Case_In_M</td><td> coefficient in the equation h = hcoeff*(T/Tdes)^0.23*(W/Wdes)^0.8 used to evaluate the convective heat transfer coefficient for the inner surface of the engine case [Btu/(sec-ft^2-degR)]</td></tr>
	<tr><td>Wdes_Case_In_M</td><td> mass flow rate at a design point (known point) used to normalize the mass flow rate in the convective heat transfer coefficient model for the inner surface of the engine case [slug/sec]</td></tr>
	<tr><td>Tdes_Case_In_M</td><td> temperature at a design point (known point) used to normalize the temperature in the convective heat transfer coefficient model for inner surface of the engine case [degR]</td></tr>
	<tr><td>Wc_Case_In_Data_M</td><td> Non-dimensional mass flow rate (W/Wdes) array used in interpolating the convective heat transfer coefficient for the inner surface of the engine case [-] (sx1)</td></tr>
	<tr><td>Tc_Case_In_Data_M</td><td> Non-dimensional temperature (T/Tdes) array used in interpolating the convective heat transfer coefficient for the inner surface of the engine case [-] (tx1) </td></tr>
	<tr><td>h_Case_In_Data_M</td><td> Matrix of convective heat transfer coefficients for the inner surface of the engine case with rows corresponding to Wc_Case_In_Data_M and columns corresponding to Tc_Case_In_Data_M [Btu/(sec-ft^2-degR)] (sxt)</td></tr>
	<tr><td>h_Const_Case_Out_M</td><td>check to use the constant h_Case_Out_M as the convective heat transfer coefficient for the outer surface of the engine case</td></tr>
	<tr><td>h_Eqn_Case_Out_M</td><td>check to use the equation h = hcoeff*(T/Tdes)^0.23*(W/Wdes)^0.8 to determine the convective heat transfer coefficient for the outer surface of the engine case</td></tr>
	<tr><td>h_Data_Case_Out_M</td><td>check to use the data arrays Wc_Case_Out_Data_M, Tc_Case_Out_Data_M, and h_Case_In_Data_M to interpolate the convective heat transfer coefficient for the outer surface of the engine case</td></tr>
	<tr><td>h_Case_Out_M</td><td> constant convective heat transfer coefficient for the outer surface of the engine case [Btu/(sec-ft^2-degR)]</td></tr>
	<tr><td>hcoeff_Case_Out_M</td><td> coefficient in the equation h = hcoeff*(T/Tdes)^0.23*(W/Wdes)^0.8 used to evaluate the convective heat transfer coefficient for the outer surface of the engine case [Btu/(sec-ft^2-degR)]</td></tr>
	<tr><td>Wdes_Case_Out_M</td><td> mass flow rate at a design point (known point) used to normalize the mass flow rate in the convective heat transfer coefficient model for the outer surface of the engine case [slug/sec]</td></tr>
	<tr><td>Tdes_Case_Out_M</td><td> temperature at a design point (known point) used to normalize the temperature in the convective heat transfer coefficient model for outer surface of the engine case [degR]</td></tr>
	<tr><td>Wc_Case_Out_Data_M</td><td> Non-dimensional mass flow rate (W/Wdes) array used in interpolating the convective heat transfer coefficient for the outer surface of the engine case [-] (ux1)</td></tr>
	<tr><td>Tc_Case_Out_Data_M</td><td> Non-dimensional temperature (T/Tdes) array used in interpolating the convective heat transfer coefficient for the outer surface of the engine case [-] (vx1) </td></tr>
	<tr><td>h_Case_Out_Data_M</td><td> Matrix of convective heat transfer coefficients for the outer surface of the engine case with rows corresponding to Wc_Case_Out_Data_M and columns corresponding to Tc_Case_Out_Data_M [Btu/(sec-ft^2-degR)] (uxv)</td></tr>
	<tr><td>Ri_Case_M</td><td>inner radius of the structural layer of the engine case [ft]</td></tr>
	<tr><td>L_Shroud_M</td><td>Distance between the inner surface of the shroud and the inner surface of the engine case [ft]</td></tr>
    <tr><td>alpha_TempDependence_Case_M</td><td>temperature dependence of the thermal expansion coefficient of the structural layer of the engine case. When unchecked the constant thermal expansion coefficient alpha_Case_M is used and when checked the thermal expansion coefficient is interpolated each time-step based on temperature and thermal expansion coefficient data given by Talpha_Case_Data_M and alpha_Case_Data_M</td></tr>
	<tr><td>alpha_Case_M</td><td>constant thermal expansion coefficient for the engine case [1/degR)]</td></tr>
	<tr><td>Talpha_Case_Data_M</td><td>temperature array for interpolating the thermal expansion coefficient of the engine case [degR] (wx1)</td></tr>
	<tr><td>alpha_Case_Data_M</td><td>thermal expansion coefficient array correspondeing to Talpha_Case_Data_M for interpolating the thermal expansion coefficient of the engine case [1/degR] (wx1)</td></tr>
</table>
<br>


